This paper investigates the effects of surface roughness on the convective stability behavior of boundary-layer flow over a rotating disk. An enforced axial flow and the Miklavčič and Wang (MW) model of roughness are applied to this flow. The effects of both anisotropic and isotropic surface roughness on the distinct instability properties of the boundary-layer flow over a rotating disk will also be examined for this model. It is possible to implement these types of roughness on this geometric shape while considering an axial flow. This approach requires a modification for the no-slip condition and that the current boundary conditions are partial-slip conditions. The Navier–Stokes equations are used to obtain the steady mean-flow system, and linear stability equations are then formulated to obtain neutral stability curves while investigating the convective instability behavior for stationary modes. The stability analysis results are then confirmed by the linear convective growth rates for stationary disturbances and the energy analysis. The stability characteristics of the inviscid type I (or cross-flow) instability and the viscous type II instability are examined over a rough, rotating disk within the boundary layer at all axial flow rates considered. Our findings indicate that the radial grooves have a strong destabilizing effect on the type II mode as the axial flow is increased, whereas the concentric grooves and isotropic surface roughness stabilize the boundary-layer flow for the type I mode. It is worth noting that the flows over a concentrically grooved disk with increasing enforced axial flow strength are the most stable for the inviscid type I instability.
References
1.
L.
Sirovich
and S.
Karlsson
, “Turbulent drag reduction by passive mechanisms
,” Nature
388
, 753
–755
(1997
).2.
P.
Carpenter
, “The right sort of roughness
,” Nature
388
, 713
–714
(1997
).3.
J. M.
Owen
and R. H.
Rogers
, Flow and Heat Transfer in Rotating Disc Systems
(Rotor-Stator Systems Research Studies
, Taunton
, Somerset
, UK
, 1989
).4.
H.
Schlichting
and K.
Gersten
, Boundary-Layer Theory
, 8th ed. (Springer
, 2000
).5.
M.
Wimmer
, “Viscous flows and instabilities near rotating bodies
,” Prog. Aerosp. Sci
25
, 43
(1988
).6.
W. E.
Gray
, “The nature of the boundary layer flow at the nose of a swept wing
,” RAE TM Aero Report No. 255
(Farnbourough, UK
, 1952
).7.
N.
Gregory
, J. T.
Stuart
, and W. S.
Walker
, “On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk
,” Philos. Trans. R. Soc. London
248
(943), 155
–199
(1955
).8.
M. R.
Malik
, “The neutral curve for stationary disturbances in rotating-disk flow
,” J. Fluid Mech.
164
, 275
–287
(1986
).9.
P.
Hall
, “An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc
,” Proc. R. Soc. London, Ser. A
406
, 93
(1986
).10.
B. I.
Fedorov
, G. Z.
Plavnik
, I. V.
Prokhorov
, and L. G.
Zhukhovitskii
, “Transitional flow conditions on a rotating disk
,” J. Eng. Phys. Thermophys.
31
, 1448
–1453
(1976
).11.
W. B.
Brown
, “A stability criterion for three-dimensional laminar boundary layers
,” in Boundary Layer and Flow Control
, edited by G. V.
Lachmann
(Elsevier
, 1961
), pp. 913
–923
.12.
M. R.
Malik
, S. P.
Wilkinson
, and S. A.
Orszag
, “Instability and transition in rotating disk flow
,” AIAA J.
19
, 1131
–1138
(1981
).13.
S. P.
Wilkinson
and M. R.
Malik
, “Stability experiments in the flow over a rotating disk
,” AIAA J.
23
, 588
–595
(1985
).14.
A. J.
Colley
, P. J.
Thomas
, P. W.
Carpenter
, and A. J.
Cooper
, “An experimental study of boundary-layer transition over a rotating, compliant disk
,” Phys. Fluids
11
, 3340
–3352
(1999
).15.
A. J.
Colley
, P.
Carpenter
, P. J.
Thomas
, R.
Ali
, and F.
Zoueshtiagh
, “Experimental verification of the type-II-eigenmode destabilization in the boundary layer over a compliant rotating disk
,” Phys. Fluids
18
, 054107
(2006
).16.
T. C.
Corke
and K. F.
Knasiak
, “Stationary travelling cross-flow mode interactions on a rotating disk
,” J. Fluid Mech.
355
, 285
–315
(1998
).17.
S.
Jarre
, P. L.
Gal
, and M. P.
Chauve
, “Experimental study of rotating disk flow instability. II. Forced flow
,” Phys. Fluids
8
, 2985
(1996
).18.
T. C.
Corke
, E. H.
Matlis
, and H.
Othman
, “Transition to turbulence in rotating disk boundary layers convective and absolute instabilities
,” J. Eng. Math.
57
, 253
–272
(2007
).19.
F.
Zoueshtiagh
, R.
Ali
, A. J.
Colley
, P. J.
Thomas
, and P. W.
Carpenter
, “Laminar-turbulent boundary-layer transition over a rough rotating disk
,” Phys. Fluids
15
, 2441
–2444
(2003
).20.
A. J.
Cooper
, J. H.
Harris
, S. J.
Garrett
, M.
Özkan
, and P. J.
Thomas
, “The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
,” Phys. Fluids
27
, 014107
(2015
).21.
T.
Watanabe
, H. M.
Warui
, and N.
Fujisawa
, “Effect of distributed roughness on laminar-turbulent transition in the boundary layer over a rotating cone
,” Exp. Fluids
14
, 390
–392
(1993
).22.
M. S.
Yoon
, J. M.
Hyun
, and J. S.
Park
, “Flow and heat transfer over a rotating disk with surface roughness
,” Int. J. Heat Fluid Flow
28
, 262
–267
(2007
).23.
M.
Miklavčič
and C.
Wang
, “The flow due to a rough rotating disk
,” Z. Angew. Math. Phys.
55
, 235
–246
(2004
).24.
B.
Alveroğlu
, A.
Segalini
, and S. J.
Garrett
, “The effect of surface roughness on the convective instability of the bek family of boundary-layer flows
,” Eur. J. Mech.-B/Fluids
56
, 178
–187
(2016
).25.
A. A.
Alqarni
, B.
Alveroglu
, P. T.
Griffiths
, and S. J.
Garrett
, “The instability of non-newtonian boundary-layer flows over rough rotating disks
,” J. Non-Newtonian Fluid Mech.
273
, 104174
(2019
).26.
S. J.
Garrett
, A. J.
Cooper
, J. H.
Harris
, M.
Ozkan
, A.
Segalini
, and P. J.
Thomas
, “On the stability of von kármán rotating-disk boundary layers with radial anisotropic surface roughness
,” Phys. Fluids
28
, 014104
(2016
).27.
S. J.
Garrett
, J.
Harris
, and P. J.
Thomas
, “On the effect of distributed roughness on transition over rotor-stator devices
,” in Proceedings of the INternational Council of the Aeronautical Sciences 2012, Brisbane, Australia
(ICAS, 2012
), p. 18
.28.
Z.
Hussain
, S. J.
Garrett
, and S. O.
Stephen
, “The instability of the boundary layer over a disk rotating in an enforced axial flow
,” Phys. Fluids
23
, 114108
(2011
).29.
R.
Lingwood
and S.
Garrett
, “The effects of surface mass flux on the instability of the bek system of rotating boundary-layer flows
,” Eur. J. Mech.-B/Fluids
30
, 299
–310
(2011
).30.
R. J.
Lingwood
, “Absolute instability of the Ekman layer and related rotating flows
,” J. Fluid Mech.
331
, 405
–428
(1997
).31.
H.
Othman
and T. C.
Corke
, “Experimental investigation of absolute instability of a rotating-disk boundary layer
,” J. Fluid Mech.
565
, 63
–94
(2006
).32.
T. C.
Corke
and E. H.
Matlis
, Transition to turbulence in 3-d boundary layers on a rotating disk-triad resonance
, in Proceedings of the IUTAM Symposium on One Hundred Years of Boundary Layer Research, Göttingen, Germany
, edited by G. E. A.
Meier
and K. R.
Sreenivasan
(Springer
, 2004
).33.
J. R.
Lloyd
and E. M.
Sparrow
, “On the instability of natural convection flow on inclined plates
,” J. Fluid Mech.
42
, 465
–470
(1970
).34.
S. J.
Garrett
, “Linear growth rates of types I and II convective modes within the rotating-cone boundary layer
,” Fluid Dyn. Res.
42
, 025504
(2010
).35.
S.
Imayama
, P. H.
Alfredsson
, and R. J.
Lingwood
, “On the laminar-turbulent transition of the rotating-disk flow: The role of absolute instability
,” J. Fluid Mech.
745
, 132
–163
(2014
).36.
S. R. J.
Lingwood
and P. H.
Alfredsson
, “Instabilities of the von kármán boundary layer
,” Appl. Mech. Rev.
67
, 030803
(2015
).37.
A. J.
Cooper
and P. W.
Carpenter
, “The stability of rotating-disc boundary layer flow over a compliant wall part 1. Type I and II instabilities
,” J. Fluid Mech.
350
, 231
–259
(1997
).38.
F. T.
Smith
, “Laminar flow over a small hump on a flat plate
,” J. Fluid Mech.
57
, 803
–824
(1973
).39.
C.
Chicchiero
, A.
Segalini
, and S.
Camarri
, “Triple-deck analysis of the steady flow over a rotating disk with surface roughness
,” Phys. Rev. Fluid
6
, 014103
(2021
).40.
R.
Miller
, P.
Griffiths
, Z.
Hussain
, and S.
Garrett
, “On the stability of a heated rotating-disk boundary layer in a temperature-dependent viscosity fluid
,” Phys. Fluids
32
, 024105
(2020
).41.
B.
Alveroğlu
, “The convective instability of the BEK system of rotating boundary-layer flows over rough disks
,” Ph.D. thesis (University of Leicester
, 2016
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
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